Formal ANOVA

1. Chapter 3 introduced how we will calculate the treatment effects. What do we mean by “effect”?
   

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• Level of measurement of response variable
• Six Fisher Assumptions
• Informal ANOVA code: Assembly line metaphor

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Categorical

• nominal: categorical variable whose levels have no ordering.
  • gender, race, etc.
• ordinal: categorical variable whose levels have an order.
  • education level

Numerical

• interval: numerical variable where we assume the distance between points is equal. No true zero.
  • scores on a “self-esteem” scale, measured from 1 to 7
• ratio: numerical variable that has a true zero point.
  • students’ times to complete cognitive task
  • enzyme concentration

• See code 02-Informal ANOVA from the course website
• Link to code.

We assume every observation in a similar condition is affected exactly the same. (Gets the same true score).

For example,

animals_sim <- animals %>%
  mutate(benchmark = mean(calm)) %>%
  group_by(animal) %>%
  mutate(animal_mean = mean(calm),
         aminal_effect = animal_mean - benchmark) #every "dog" observation gets the same effect

We add the effects as we go down the assembly line.

All effects are added on.

calm_sim = benchmark 
         + aminal_effect 
         + cue_effect 
         + interaction_effect 
         + student_effect 

The piece of code for adding error is not dependent on which condition the observations is in. Every condition gets the same standard deviation, here 0.65.

 + rnorm(68, 0, 0.68) #rnorm(n, mean, sd = 0.65)

Takes 68 independent draws from a normal distribution.

 + rnorm(68, 0, 0.68) #rnorm function assumes independence

It's rnorm(), and not rbinom() or rpois()…

 + rnorm(64, 0, 0.68)

The second argument is the mean.

 + rnorm(64, 0, 0.68) #rnorm(n, mean = 0, sd)